Surprised by Euthyphro's willingness to prosecute his father on so questionable a charge, Socrates remarks that Euthyphro must have a very exact understanding of religious matters to proceed in such a way. Euthyphro proudly claims that he is an expert in all religious matters, and that this is what differentiates him from the common man. In response to this claim, Socrates suggests that perhaps Euthyphro could teach him about religious matters. That way, if Meletus were to prosecute him, Socrates could say that he is now under the tutelage of Euthyphro, whose authority on these matters is unquestionable. If Meletus were to prosecute him even so, Socrates could point out that Euthyphro is in fact the one responsible for teaching him and that Meletus should prosecute Euthyphro instead. Euthyphro encourages this suggestion, pointing out that with his expertise in religious matters, Meletus' claims could not stand up long against Socrates in court.
Socrates insists that Euthyphro begin to instruct him regarding what is holy and what is unholy. Socrates has Euthyphro agree with him that there must be one form or standard by which everything holy is holy and everything unholy, by contrast with the holy, is unholy. That is, all holy deeds must be holy by virtue of some feature or other that all holy deeds share in common. Socrates asks Euthyphro what this feature is.
Euthyphro suggests that prosecuting those who commit injustices is holy, and not prosecuting them is unholy. Here, Euthyphro appeals to two Greek myths, noting that Zeus imprisoned his father, Kronos, and that Kronos castrated his father, Uranus. Zeus is the best and most just of all the gods, and so if he behaves rightly in imprisoning his father for injustice, Euthyphro should be lauded for following this example.
Socrates is somewhat surprised by Euthyphro's example, and asks him if he believes literally all the myths about the gods--that they quarrel and have great battles as is depicted in Greek art and told in the stories of Homer and Hesiod. Euthyphro confirms that he believes all this and more. He says that his knowledge of divine matters is such that he could teach Socrates a great deal that Socrates did not know about the gods.
Socrates suggests that perhaps that can wait for another time. His present concern is with the definition of holiness, which he feels Euthyphro has not yet properly dealt with. That one should prosecute those who commit injustices is holy is merely an example of a holy act, and not a definition of holiness itself. Euthyphro concedes that there are a great many holy deeds that do not consist in prosecuting a religious offender. Socrates then urges Euthyphro to give a more general definition and to identify a standard by which all holy deeds can be recognized as holy.
Socrates is clearly setting up Euthyphro in a very characteristic manner. There is an obvious touch of irony (evident to all but Euthyphro, presumably) in the way Socrates praises Euthyphro's knowledge of divine matters and asks to be taught by him. He does not actually expect to learn from Euthyphro, but rather intends to lead Euthyphro out of his false confidence in his supposed knowledge and toward a wiser and more humble acknowledgment of his own ignorance. Socrates' method is not to tell Euthyphro that he is mistaken in claiming to be an expert on religious matters, but rather to show him through questioning. By asking for a general definition of what is holy, Socrates will show that Euthyphro has no such understanding at all.
An important question raised by Socrates' appeal to Euthyphro--to present a general standard by which all holy deeds can be recognized as holy--is how much Plato's Theory of Forms is present in this dialogue. The Theory, roughly stated, is that for every abstract idea (and arguably for material objects as well) there is a corresponding Form: the Form of Beauty, the Form of Justice, the Form of Courage, etc. Anything in the sensible world which has a certain quality only has that quality by virtue of its participating in the Form associated with that quality. While the sensible world is imperfect and perishable, the world of Forms is a transcendent reality of perfection and immortality. The goal of the philosopher, according to Plato's theory, is to properly understand and appreciate these Forms, freeing his soul from the mundane material world.
The Theory of Forms is best exemplified in Plato's great middle period dialogues, such as the Phaedo and the Republic. The early dialogues, among which the Euthyphro is counted, are centered around Socrates' teachings and do not yet deal with the Theory of Forms. Plato's theory is nevertheless present in this section, however. In asking Euthyphro to define holiness according to some standard common to all things holy, Plato is employing much of the vocabulary he would later use in his more explicit discussions of the Theory. Still, there is no reason that we should read the technical aspects of the Theory of Forms into this discussion, since Socrates' questioning makes sense even if we read it in an entirely non-technical manner. The Euthyphro is a paradigmatic early dialogue; it would be odd to ascribe Platonic theories to such a work.
We can easily see Socrates' conviction that true knowledge of a concept comes only when we can properly define it. That is, we cannot say we know what holiness is if, as Euthyphro does in this section, we only point to a few instances of things we consider holy. Rather, we must be able to give an overarching definition that will presumably help us to explain why particular instances of holiness count as such. It has been suggested that Plato, in later dialogues, will ultimately conclude that the Theory of Forms is the only way to provide satisfactory definitions. The Euthyphro and other early dialogues end at an impasse, where the interlocutor is made to realize that he does not understand what he claimed to know, but no positive definition is given. A Platonist might suggest that no positive definition can be given without the Theory of Forms.
The brief discussion regarding Euthyphro's literal treatment of the Greek myths may seem out of place here, but it will be brought back into the dialogue at a later time. It should be noted that Athenians at this time generally did not believe the myths to be literally true. Euthyphro's proud and dogmatic insistence that he does know the truth regarding these matters only makes him appear less credible. (His position might be compared in modern times to a religious fundamentalist.)
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.