Socrates asks Euthyphro once more to give a definition of holiness, since his earlier definition, that what is holy is what is approved of by the gods, does not seem to hold. Euthyphro complains that Socrates makes his arguments go around in circles and never stay in place so that he no longer knows where he stands. Socrates corrects Euthyphro, pointing out that he is only asking questions, and it is Euthyphro's answers and Euthyphro's arguments that are going around in circles.
Socrates then urges Euthyphro to continue the inquiry. To help him along, he suggests that perhaps everything that is holy is just. He then asks whether, in turn, everything that is just is holy, or whether only part of what is just is holy. To illustrate his point, he quotes a line of poetry: "where is found fear, there is also found shame." Socrates disagrees with this line, pointing out that there are many things that we fear, such as disease and poverty, of which we are not necessarily ashamed. However, he points out, where there is shame, there is also fear: a feeling of shame can be characterized as a fear of a bad reputation. His question regarding justice and holiness is similar: his suggestion is that where there is holiness, there is also justice, but that perhaps there are cases of justice where holiness is not a concern. Euthyphro agrees with this suggestion.
Then, if holiness is a division of justice, Socrates urges Euthyphro to point out what kind of division of justice holiness is. That is, if we can identify that part of justice which is included under holiness, then we will have an adequate definition of holiness. Euthyphro suggests that the part of justice that is concerned with looking after the gods is holiness, whereas the part of justice that is concerned with looking after men is not.
Socrates is somewhat satisfied with this definition, but asks Euthyphro if he could be clearer as to what he means by "looking after." For instance, a groom looks after a horse, a kennel master looks after a dog, and a cattle farmer looks after cattle. These animals benefit from being looked after by these sorts of people; they are made better, whereas the ordinary person would probably do more harm than good. Socrates asks if Euthyphro similarly thinks that the gods are made better by deeds of holiness, and that every time Euthyphro does something holy, the gods are somehow improved. Euthyphro denies that he means this sort of relationship, suggesting instead that we look after the gods in the way that a slaves look after their masters.
Socrates points out that people who serve are always being used to achieve some sort of goal: service to a shipbuilder, for instance, is done with the goal of building a ship. What, Socrates asks, is the goal of the gods which we help them to achieve? Euthyphro evades the question, suggesting that the gods use us for a multitude of reasons. Socrates replies that we could just as well say a general uses his underlings for a multitude of reasons, but that the principal reason is still the goal of winning a war. Thus, he presses Euthyphro once more to identify the one goal that our service to the gods helps them to achieve.
Euthyphro's complaints to Socrates that his arguments are being made to go in circles and are not staying still is a further illustration of Socrates' method. Socrates sternly points out to Euthyphro that it is Euthyphro's own arguments and answers that are going in circles. Socrates' role is only that of a questioner, and Euthyphro is being made to take full responsibility for the direction that the dialogue takes. This also explains why Socrates ironically insists that Euthyphro teach him about holiness at the beginning of the dialogue. If Euthyphro is the teacher and Socrates is only the student asking questions, then Euthyphro must take responsibility for the material that he teaches.
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.