I'm reading and writing about Nietzsche's Death of God and the ethical systems preceding the enlightenment. One major problem that we face is the lack of, for the lack of a better term, "grounding" of current moral system. Consider the three major ethical traditions now

Utilitarianism - Any high level version i.e. Rule Utilitarianism will collapse into Act Utilitarianism

Deontology - Lack of context in making ethical decisions

Virtue Ethics - Slightly better but still relativistic.

Furthermore, both 1 and 2 don't have axioms that appeal to fundamental moral intuitions. Before even talking about what is moral, we have to examine whether morality is objective. This is where a lot of the criticism occur especially from Moral Anti-realists or immoralists.

I believe we're looking at the issue in a different angle. We don't need to prove that Morality is objective, in its complete epistemological sense. That problem of true objectivity may never be solved. Science, for example, is reasonably objective. Mainly due to the problem of induction. If we prove that Morality is objective in an equivalent manner, there could be a ground to based it off on. Here's my Primitive Argument. Feedback very much appreciated.

Preliminaries

Let C denote the context (i.e. the circumstance being referred to). Let K be the set of knowns (i.e. everything the rational agent knows about C; sensory inputs and common virtues are examples of this). Let M denote the method grounded in rationality and H be the hypothesis i.e. a questions that has either true or false answers. The conventional usage of mathematical functions maybe used here. Either M(C, K, H) = true or M(C, K, H) = false

Virtue : A Quality deemed to be Good

Vice: A Quality deemed to be Bad

True Objectiveness : The Statement at hand is known to be true, or false, regardless of what any rational agent might ascertain.

Lemma 1: Any Scientific conclusion doesn't hold the property of "True Objectiveness"

Proof. Let's take a hypothetical context C. The knowns while using the scientific method are the senses, denoted here by K_{S}. Assume we reach a conclusion M(C,K_{S}, H), regarding hypothesis H, B for instance. Let's say a non-human being approaches with a new sense S_{N} and analyzes the context. There is very well the possibility that M(C, K_{S} + {S_{N}}, H) offers a new conclusion - B_{N}. Hence, we can't claim complete objectivity over the scientific method.

Note that this is a different way to put forth the problem of induction.

Reasonable Objectiveness : Science is assumed to be reasonably objective

Theorem 1 (The Cultural Argument): There are a set of moral knowns, M_{K} either virtues or vices, that are part of human essence

Proof. Let's outline the argument.

Premise 1: Morality is a concept that exists in human society

The idea of what one ought to do exists in society, whether the answer maybe agreed upon or differs.

Premise 2: Significant differences in Morality can be seen across different cultures

Cultures could mean anything from Religion, Tribes to even different languages. For instance, the morality of Buddhism and Islam is significantly different due to the cultural differences (religion here)

Premise 3: Throughout human cultures, a common set of virtues or vices are shared

There are cultural arguments to be placed here. But inductive anthropological evidence is already present.

Is It Good to Cooperate? Testing the Theory of Morality-as-Cooperation in 60 Societies - https://www.journals.uchicago.edu/doi/full/10.1086/701478

Conclusion: Common set of moral knowns are independent of culture and therefore part of the human essence

Primitive Moral Method: The Right thing is to uphold the moral knowns, unless conflicting virtues and/or vices exist in the context.

Lemma 2: Primitive Moral Method is reasonably objective"

Proof. Suppose the primitive moral method isn't reasonably objective. That means the answer, it only applies to moral questions with answer by definition, must be conflicting dependent on observers. But both the observers can't be human, because inductive anthropological evidence dictates that they share the common virtues necessary. Hence a non-human agent who is rational has to exist with a new moral known M_{N} , that must gather new conclusions. But this is the reasonable objectivity permitted by the scientific method. Therefore, a contradiction arises. Q.E.D.

After this I have a similar argument where morality of specific context require upholding virtues embedded in that social context i.e. the telos. For instance, Schools are for learning, Hospitals are for healing etc. Here an equivalency can be drawn between this and language, similar to Wittgenstein.

Goal is to show that a moral method like that is reasonable objectivity similar to science and language. Hence if we reject it, we have to reject science and language.

Would love some feedback. Thank you!