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The Euthyphro takes place right before Socrates' trial, and right outside of the law-court, where he runs into the very guy the dialogue is named after. They get into a tangled discussion about the nature of "piety" or "holiness" - one which ranges over a number of topics and arguments.
In the process, Socrates articulates a problematic that has come to be recognized as a major issue in the Philosophy of Religion. It's called the "Euthyphro dilemma" - and if you listen to the episode on it, you'll see why it's so important!
Here are the three lectures:
As a reference for what you're listening to, you might want to get The Last Days of Socrates, which includes the Apology, Crito, Euthyphro, and Phaedo. The podcast lectures are designed to help you understand some of the key concepts of philosophical works. So don't deprive yourself of the pleasure of reading Plato's dialogues!
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