In contemporary philosophy, “The Euthyphro Problem” is a question about why things are good and about the difficulties in (a caricature of) divine command theory, but this is a very different question from the question raised in the Plato’s dialogue Euthyphro, which treats of various dilemmas that arise in trying to define what piety is. Euthyphro continually fails to define piety by continually failing to describe a being that would be worthy of piety, which is to say that he never comes up with an adequate notion of the sort of being that deserves to be worshiped as divine. This is hardly a hidden teaching of the dialogue, since the first definition of piety that Euthyphro gives is:
Piety is what I am doing, charging my father with murder…. For do not men regard Zeus as the best and most righteous of the gods?-and yet they admit that he bound his father (Cronos) because he wickedly devoured his sons, and that he too had punished his own father (Uranus) for a similar reason, in a nameless manner.
To which Socrates responds:
This is the reason, Euthyphro, why I am a defendent in this case – that I cannot accept these stories about the gods.
In other words, Socrates rejects the whole basis of Euthyphro’s piety, and he suspects that this is the reason why the Athenians are putting him on trial. The dialogue is therefore a call to reform a false notion of what is divine in order to articulate the nature of a being to whom piety would be due.
Both Socrates and Euthyphro are working from the supposition that one and the same thing or action cannot not be both pious and impious. Following this, the problems that arise in finding an object of piety arise mainly from the problems of understanding the act of the divine will, that is, divine love. If a pious action is an object of divine love, then we require complete singularity and unanimity of the divine will; for without complete and unchanging unanimity, one and the same action can be both pious and impious. Euthyphro could have avoided this problem by stipulating that one and the same action could be pious or not, depending on which god one related it to (and so, famously, killing Trojans would be pious to Athena and impious to Hera), but Euthyphro, much to his credit, is not willing to accept such relativism. There might be some actions that are loved by one god and hated by another, but such actions cannot exhaust all pious actions, and certainly not the loftiest such actions. However misguided Euthyphro might be about the piety of his own action, he nevertheless is right to never abandon the idea that some actions are just pious, now and forever. Euthyphro isn’t willing to accept the logical consequences of this opinion, however. It makes no sense to think that the pious is not somehow an object of divine love; but if something is absolutely and changelessly pious, what then? Euthyphro would probably make an even stronger claim: there are things which admit no possibility of being impious. But it is very hard to harmonize such an idea with a multiplicity of divine wills, and therefore with a multitude of divinities; and it even becomes difficult to harmonize with a single divinity that could change his will from one thing to another. This, of course, opens a new difficulty and problem, which Socrates develops with a second series of arguments.