Axioms are only arbitrary in terms of the logical system they are involved in. If they conflict with other axioms, one of them has to go. So the choice of axioms isn't totally arbitrary, even at the level of logic.
When it's time to take an idealized theory and use it to make predictions about the real world, we first have to check that the axioms match our sense data. If they don't, it's not an applicable theory. That removes another degree of arbitrariness when putting any theory into practice.
"Feeling" good or bad is the bedrock of morality. From the vantage point of the human mind, our entire experience is colored with judgement. e.g. This is net good, that is net bad, etc. There are interesting questions to ask about how that evolved, or why it presents itself in consciousness, but it is first and foremost just a fact about the human experience.
That isn't arbitrary. A human cannot will their experience to stop containing judgements.
So yes, many people have come up with many theories about morality, ethics, and meta-ethics, but we can and should discard any of them that don't have their axioms satisfied by ground truth.
When it's time to take an idealized theory and use it to make predictions about the real world, we first have to check that the axioms match our sense data. If they don't, it's not an applicable theory. That removes another degree of arbitrariness when putting any theory into practice.
"Feeling" good or bad is the bedrock of morality. From the vantage point of the human mind, our entire experience is colored with judgement. e.g. This is net good, that is net bad, etc. There are interesting questions to ask about how that evolved, or why it presents itself in consciousness, but it is first and foremost just a fact about the human experience.
That isn't arbitrary. A human cannot will their experience to stop containing judgements.
So yes, many people have come up with many theories about morality, ethics, and meta-ethics, but we can and should discard any of them that don't have their axioms satisfied by ground truth.