Euthyphro ends up agreeing that the definitions of piety he has proposed are inadequate. How would you explain what was wrong with them?

 In Plato's dialogue "Euthyphro," Socrates and Euthyphro discuss the nature of piety or holiness. Throughout their conversation, Euthyphro proposes several definitions of piety, but Socrates finds problems with each one.

1. The first definition Euthyphro offers is that piety is what he is doing now, prosecuting his own father for murder. Socrates challenges this by pointing out that this is just an example of a pious action, not a definition of piety itself. Euthyphro's response doesn't offer a general principle that could be applied to all pious actions.

2. Euthyphro's second definition is that piety is what is dear to the gods. Socrates raises the problem of the gods’ disagreement: since the gods often have conflicting views, what is dear to one god might not be dear to another. Thus, this definition could lead to the same action being both pious and impious, which seems contradictory.

3. Euthyphro then revises his definition, saying that piety is what all the gods love, and impiety is what all the gods hate. Socrates then presents the "Euthyphro Dilemma": Is something pious because the gods love it, or do the gods love it because it is pious? This is meant to question whether piety is inherently good or just good because the gods approve of it.

4. Socrates argues that if the gods love pious actions because they are pious, then there must be some standard of piety that is independent of the gods' love. This means that Euthyphro hasn't really defined piety; rather, he has just described a characteristic of pious actions (being loved by the gods) without explaining what makes them pious in the first place.

Each time, Socrates demonstrates that Euthyphro's definitions either rely on examples that don't provide a general principle or create logical inconsistencies. The primary issue with Euthyphro's definitions, as per Socratic reasoning, is that they fail to capture the essence of piety and do not hold up to critical interrogation.