What did Socrates and Euthyphro ultimately conclude about holiness during their discussion?

During the dialogue between Socrates and Euthyphro, they engage in an examination of the concept of holiness, but ultimately, they do not arrive at a clear or mutually agreed-upon definition. Throughout their discussion, Socrates challenges Euthyphro's attempts to define holiness, probing deeper into the nuances of the definitions provided.

As the conversation progresses, Euthyphro suggests that holiness is what is loved by the gods, but Socrates raises the question of whether the gods love it because it is holy, or if it is holy because the gods love it. This leads to a cycle of definitions that fails to satisfy the philosophical inquiry Euthyphro is subjected to, leaving both participants frustrated. They come to realize the complexity and ambiguity surrounding the concept of holiness, which leads to their inability to reach a conclusive understanding. Thus, it is evident that their discussion ends without a definitive conclusion about holiness, which highlights the limitations of their philosophical exploration on the subject.