How can Plato’s “Euthyphro" be used to help understand the “Allegory of the Cave”?

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In Plato’s Euthyphro, Socrates is headed to his trial that will decide whether he lives or dies. On the way to court, Socrates meets Euthyphro who is also on his way to court but for an entirely different reason. Euthyphro is pressing charges against his own father for manslaughter. Against the backdrop of this conversation about whether or not Euthyphro should try his own father in court, Socrates and Euthyphro discuss the definition of piety. In the “Allegory of the Cave,” a story written in the Republic, Socrates imagines that there exists a dark cave where all humanity lives (514). They have lived there since childhood “fixed in the same place” with their necks and legs in chains (515). One day, a prisoner, freed from his chains, escapes the cave to find the truth of his own existence, and the nature of reality itself. Both stories are very different from one another. However, they both have one essential thing in common. They are both about a search for truth. In this way, Plato’s Euthyphro will be used to help understand better the Allegory of the Cave....

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