Advantages
Moral realism allows the ordinary rules of logic (modus ponens, etc.) to be applied straightforwardly to moral statements. We can say that a moral belief is false or unjustified or contradictory in the same way we would about a factual belief. This is a problem for expressivism, as shown by the Frege-Geach problem.
Another advantage of moral realism is its capacity to resolve moral disagreements: If two moral beliefs contradict one another, realism says that they cannot both be right, and therefore everyone involved ought to be seeking out the right answer to resolve the disagreement. Contrary theories of meta-ethics have trouble even formulating the statement "this moral belief is wrong," and so they cannot resolve disagreements in this way.
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