Socrates encounters Euthyphro outside the court of Athens. Socrates has been called to court on charges of impiety by Meletus, and Euthyphro has come to prosecute his own father for having unintentionally killed a murderous hired hand. Socrates flatters Euthyphro, suggesting that Euthyphro must be a great expert in religious matters if he is willing to prosecute his own father on so questionable a charge. Euthyphro concurs that he does indeed know all there is to be known about what is holy. Socrates urges Euthyphro to instruct him and to teach him what holiness is, since Euthyphro's teaching might help Socrates in his trial against Meletus.
First, Euthyphro suggests that holiness is persecuting religious offenders. Socrates finds this definition unsatisfying, since there are many holy deeds aside from that of persecuting offenders. He asks Euthyphro instead to give him a general definition that identifies that one feature that all holy deeds share in common. Euthyphro suggests that what is holy is what is agreeable to the gods, in response to which Socrates points out that the gods often quarrel, so what is agreeable to one might not be agreeable to all.
Euthyphro's most important attempt to define holiness comes with his suggestion that what is holy is what is approved of by all the gods. Socrates sets up a rather elaborate argument to show that the two cannot be equivalent. What is holy gets approved of by the gods because it is holy, so what is holy determines what gets approved of by the gods. And what gets approved of by the gods in turn determines what is approved of by the gods. It follows from this reasoning that what is holy cannot be the same thing as what is approved of by the gods, since one of these two determines what gets approved of by the gods and the other is determined by what gets approved of by the gods.
Euthyphro is next led to suggest that holiness is a kind of justice, specifically, that kind which is concerned with looking after the gods. Socrates wonders what Euthyphro means by "looking after the gods." Surely, the gods are omnipotent, and don't need us to look after them or help them in any way. Euthyphro's final suggestion is that holiness is a kind of trading with the gods, where we give them sacrifices and they grant our prayers. Our sacrifices do not help them in any way, but simply gratify them. But, Socrates points out, to say that holiness is gratifying the gods is similar to saying that holiness is what is approved of by the gods, which lands us back in our previous conundrum. Rather than try to find a better definition, Euthyphro leaves in a huff, frustrated by Socrates' questioning.
Socrates is treating Euthyphro as the teacher when in fact Socrates is teaching Euthyphro
Plato suggesting that there is no such thing as a definition of holiness, that there is no one feature that all holy deeds have in common?
What Plato/Socrates is challenging is Euthyphro's/everyone's knowledge or assumed knowledge of anything, not the can we know anything idea, but have we challenged our beliefs? Are we sure that the conclusion we hold is conclusion enough? Peirce and James pick this up again a few years later.