[jacobr1]

Metaethics has been in discourse on this for some time. I think most the prevalent systems do reduce down to a small set of axioms (foundationalist propose a strong form of this), or a least a set of internal consistent, self-reinforcing propositions (coherentism, which doesn't necessary presume a prepositional hierarchy).

Some of the more interesting (to me) arguments of the realists/naturalists (the justification question rather than the ontological question above), consider there to be emergent properties from the nature of interaction between agents. Basically game-theory. Presume we all were psychopaths, but intelligent self-maximizing agents and not the irrational kind. What behaviors would maximize achieving our ends? What behaviors would we need to hold others accountable to support our ends? You can take this thought experiment pretty far to get an "emergent" moral system with first-order properties similar to those we see in real societies. I find this insufficient though, you still need some base value system. Even the psychopath example presumes a set of ends for individuals like "continued survival" and so boils down to something like a form "utilitarianism."