The Euthyphro dilemma asks, basically, if God is good becaue He answers to some Good Law, and this goodness is Higher than him, and preexists Him in some way, or if instead goodness is just our word for what God declares His preference for, thus rendering goodness arbitrary. The implication (what makes it a dilemma) is that these are the only two options.
First of all, it seems to me that this assumes a law-based understanding of right and wrong. This isn’t often questioned, because I think that’s still the dominant understanding right now- an action is right (not wrong) if it doesn’t violate some rule of behavior, and ethics is a discussion about what those rules are, and how they are decided or discovered.
Consider Hercules. His story is caught up in a Hellenestic virtue/shame approach that admits to no law, and in fact, is a lesson in achieving virtue in open defiance of the same, in the form of the gods. Hercules did heroic feats, to be sure- but if you look closely at them, he wasn’t exactly righting wrongs, or rescuing damsels, or any other such things. His labors were characterized by the fact that nobody else could have possibily completed them. Indeed, their ultimate meaning was as penance for a wrong that the gods manipulated him into in the first place.
As far as I can tell, the goodness of him comes from self-exemplification, in this case through besting the labors. Accomplishing things like this is key to ‘who he is’. I don’t just mean it’s key to the plot of his story, though that is true too. What I mean is, if we could imagine Hercules from his own point of view, conquering each labor would be essential to maintaining his own self-image- of living up to his idealized notion of himself. If he failed in a labor, or balked and didn’t attempt, we could imagine This Great Hero of Greece feeling horrible shame. Not because his failure transgressed a law, or dissappointed anybody (indeed, most of the time the only people talked about who know of his labors are hoping he will fail), but rather, the shame that comes from failing one’s own standards. We see this theme repeated over and over with Greek heroes.
So, then, if Hercules is about showing himself to be indominable and superior, in the absence and defiance of external law, why do we not see him as wicked and selfish? Simply put, it is because the idea of himself that he strives to honor is something that we recognize as admirable. The man born with a great gift, beset by the capricious and arrogant Powers That Be, and using his gift to overcome the obstacles they they constantly put in front of him, is instantly respectable. We hope that in a similar position, we would behave more or less as he did- it wouldn’t make for much of a story, otherwise. It is possible that Hercules to fail in his labors, but it is not possible for him to fail and still be Hercules, in the way he strives to realize himself.
So I think here we have an example of the right and good that comes from the exemplification of one’s own respectable character. It’s a sort of virtue, defined by one’s intergrity, and recognized in a social sort of way through the appeal of the person you make yourself to be. The importance here is that we have an understanding of the good that doesn’t rely on law.
Sartre echoes this in his own way- since all free beings have an element of nothingness, we have the ability (the imperative, really) to create meaning in our own lives. Now, the impetus for him to come up with this mechanism for meaning is his conviction that meaning isn’t going to come from anywhere else, but despite that disagreement, I think there’s still something useful here for the theist to understand, in the form of a more modern exception to Euthyphro. Meaning doesn’t come from a law or else from nowhere, it comes from ourselves, and it is meaning. From Sartre’s perspective, the meaning that a man creates is in some sense arbitrary, in the way that it is completely up to us, and there is no judging as to whether or not we did a good job, other than through the reflections of society. But we don’t need to go quite that far with him. It is enough for my purposes to point out that the capacity to create meaning is tied inevitably to free will, and that free will is an irreducible facet of personhood (existing in motives, actions, and ends, but not mechanically accounted for by the interaction of them).
So, an answer to the Euthyphro dilemma could begin with recognizing that God is free, and thus, must create meaning. God creates meaning through His actions, the same as any other free being necessarily does. The meaning that God creates is what we are calling good, not some higher law that God recognizes. The meaning comes from God's unfailing ability to exemplify His own character, and it is the elements of that character that inspires us to see the meaning He creates as good, with proper understanding of it. So for example, the 10 Commandments are not themselves examples of God's goodness, but the act of giving them to the Isrealites might be.
Treating the second horn or the dilemma, God is eternal and omnipotent. Just as Hercules reacting in cowardice to his labors would be a failing of his character, there are many actions that would be failings of God’s character as well, and nothing can make God fail. So understood, what God declares to be good through His creation of meaning could not have been just anything as the dilemma asserts must be the case in the absense of higher law. God could not be or have been other than He is, and so what is good could not have been other than what it is either, even though it is based ultimately on no law. All that’s left is the inclusion of our recognition of God’s good as good, which not all people will. At the same time, we are created by this same God, so it’s natural to expect that it will resonate with the proper* expression of our own selves to do so.
- I realize of course that Sartre would disagree that an expression of ourselves can be ‘proper’, or dictated by the circumstances of our coming to exist. However, I see that as symptomatic of his atheism, and not necessary to the points I’m trying to make here.