According to many skeptics, including many philosophers, the idea that God is the foundation of morality can be refuted according to the Euthyphro dilemma (ED). Socrates, in Plato’s Euthyphro dialogue (10a), asked: “Is what is holy holy because the gods approve it, or do they approve it because it is holy?” In modern times this has been rephrased in various ways. Here’s one: “Is what is good good because God commands it, or does God command it because it is good?”
Is this a good objection? It all depends on the details. As I showed in an earlier post, “Taxonomy of Theistic Meta-ethics,” there are a variety of theories about how God or some fact about God might be the foundation for morality (or, to be more precise, moral properties). One of the oldest and simplest versions is the Divine Command Theory (DCT-D) of moral obligation: moral properties like required, permitted, and forbidden are metaphysically grounded in God’s commands. In my opinion, the ED is a successful objection to DCT-D. Probably most philosophers, including most theistic philosophers, would agree. But most theists–at least most theistic philosophers who write about metaethics–reject DCT-D as such. Indeed, while I don’t know this for sure, I suspect that the ED was one of the reasons Christian philosopher Robert Adams was motivated to develop his Modified Divine Command Theory (MDCT-D).
Can the ED be modified in other ways to refute these other theories? Perhaps. But this needs to be shown, not assumed. Woe to the skeptic who naively assumes that trotting out the ED somehow refutes all of the various theories about how morality might depend on God!
My advice: if you’re going to make an objection to a theory, make sure your objection actually applies to the theory!