At this point, Euthyphro becomes frustrated with Socrates, telling him that it is very difficult to learn about holiness with accuracy. Euthyphro instructs Socrates that it is a matter of gratifying the gods through prayer and sacrifice, and that such holiness will bring salvation and happiness to those who practice it. Socrates points out that if that is Euthyphro's view, Euthyphro could have summed things up far sooner and in far fewer words. It seems, Socrates suggests, that holiness for Euthyphro is a kind of science of sacrifice and prayer, where sacrifice is giving something to the gods and prayer is asking something of them. Euthyphro assents to this definition, suggesting that holiness is a kind of skill in trading. We get what we want from the gods through prayer, and they get what they want from us through our sacrifices.
Socrates remarks that certainly we get a great deal of good from the gods, but asks what the gods get in return. What is it, Socrates wants to know, that the gods gain from our sacrifices? Euthyphro answers that there is no way that the gods can actually benefit from our sacrifices: they are all-powerful and do not need our help. Instead, our sacrifices honor and give gratification to the gods. Socrates leads Euthyphro to assent that if he is saying the gods find our sacrifices gratifying, he is then suggesting that our sacrifices are what is approved of by the gods. But, Socrates points out, this leads us back to where we were before, asserting that what is holy is what is approved of by the gods. Either the argument put against it earlier was wrong, or the present position is also wrong.
Socrates urges Euthyphro to start again from the beginning and provide him with a more suitable definition of holiness. Frustrated, Euthyphro insists that he has a pressing appointment and uses this as an excuse to scurry off. Socrates calls after him, expressing his disappointment, and worrying that he will now be no better off in his trial against Meletus.
No new philosophical material is introduced in this section. Instead, we are given a new definition that is quickly shown to be the same argument as the earlier, unsuccessful definition. Once again, it seems that Euthyphro's arguments are going around in circles and not staying put. Rather than provide an entirely new definition, Euthyphro backs out, ending the dialogue rather abruptly. This final section is laced with irony that is quite humorous. It seems to be increasingly clear to Euthyphro that Socrates is not in fact in awe of his great knowledge, and is more interested in exposing Euthyphro's great ignorance than anything else. Euthyphro's sudden departure and flustered tone throughout this scene can be understood as signs that Euthyphro is catching on to Socrates' method.
By the end of the dialogue, we are no closer to having a definition of holiness than we were at the outset, so we might ask what we have learnt. If nothing else, we have learnt with Euthyphro that holiness is not easily defined and that perhaps we are more ignorant than we think. That this last definition turns around and appears to be another incarnation of an earlier definition might suggest that Euthyphro has exhausted his stock of definitions. When we think we have a possible definition of holiness, we are probably still on the same wrong track. A proper definition of holiness may have to wait for the Theory of Forms to be formulated (as suggested in the Commentary section of 4e - 6e).
Alternatively, we could read a much more modern line of thought into the dialogue and see Plato suggesting that there is no single feature that all holy deeds have in common. Wittgenstein has pointed out in the twentieth century that many of the words we use cannot be defined in terms of one or several features that all of its referents have in common (for instance, what feature do all games share in common?).
The one thing Euthyphro does seem to come to appreciate by the end of the dialogue is the irony Socrates has been employing throughout. He leaves in a huff as it dawns on him that Socrates has made a fool of him. Perhaps in the future, Euthyphro will be more wary of claiming certain knowledge of things. Perhaps he will be more concerned with careful thought and investigation, with humbler yet more accurate claims to knowledge. This, more than any particular doctrine, is what Socrates had to teach.
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.