Euthyphro What is Socrates' definition of piety in the Euthyphro?

The Socratic dialogue of the Euthyphro is initiated by the case of a young man who has brought charges against his father for murder. The father, hearing that a slave on his property was himself accused of murdering another man, bound the accused slave and threw him in a ditch, causing the man to die from overexposure. In Athens, there was no formal prosecutor who investigated matters and brought charges before the courts of law. Given this situation, the man's son Euthyphro decided to bring charges against his own father in a supposed show of piety. Euthyphro deems his actions to be pious, or pleasing to the gods, because he is acting as an objective judge of moral rights and wrongs. Because Euthyphro justifies his actions through a claim of piety, the question of what constitutes piety is a central, driving preoccupation of the narrative. Also, at the moment in time when the dialogue takes place, Socrates was accused of impious behavior, or denying the validity of the city's gods.

Euthyphro first defends himself by saying that piety is "doing as I am doing; that is to say, prosecuting any one who is guilty of murder, sacrilege, or of any similar crime-whether he be your father or mother, or whoever he may be-that makes no difference; and not to prosecute them is impiety. He points out that Zeus also punished Cronos, and Cronos acted against Uranus. Socrates clearly does not believe these myths about the gods are to be taken literally, and challenges Euthyphro's first definition that by acting as the gods did, he is pious.

When pressed, Euthyphro arrives at his second definition: "Piety, then, is that which is dear to the gods, and impiety is that which is not dear to them." However, this raises the fundamental question: is an action pious merely because it is loved by the gods? Or do the gods love actions because they are pious? The gods have done things which are quite impious and would...

Also, Socrates points out that the gods often have differences of opinion (given the fact that the Greeks believed in many gods, this is an additional complication of a polytheistic society). Euthyphro responds that all the gods would condemn murder, but Socrates states that even between men there are disputes as to whether a specific murderer should be convicted or not. Euthyphro refines his definition to say that piety is what is loved by all the gods and what all the gods hate is impious. But it is still not clear that the gods would 'love' Euthyphro's actions, based upon his statement.
Finally, Euthyphro states: "piety or holiness, Socrates, appears to me to be that part of justice which attends to the gods, as there is the other part of justice which attends to men." In other words, piety is treating the gods with justice such as by making burnt offerings) versus treating other human beings in a fair manner. Piety is a subset of justice. Socrates says this is not acceptable because the notion of piety attending to the gods means that men are the administrators and caretakers of the gods, like trainers are over horses, while Euthyphro believes humans are ultimately subordinate to the will of the gods.

Socrates presses onward: "And does piety or holiness, which has been defined to be the art of attending to the gods, benefit or improve them? Would you say that when you do a holy act you make any of the gods better?" In other words, if the gods are so great, why do they need obedience and attentiveness from human beings? Euthyphro suggests that this obedience is really a form of 'ministration' or tending to the gods like servants attend to their masters, which Socrates likewise says is objectionable, given that it is analogous to a shipbuilder ministering or attending to a ship, and still suggests a subordinate relationship of the gods to humans. "I wish, however, that you would tell me what benefit accrues…