The Teaching assistant, Mr. Paul Julian of FAS Harvard, has been kind enough to resent the summary. Mine was pretty far off, touché for people who has more opinions on Euthypro case.
Sample Summary of Plato’s Euthyphro
This passage opens with Euthyphro claiming that pious things are those that are loved by all the gods (with “things” presumably including acts, attitudes, characters, and so on). Socrates responds that Euthyphro’s claim admits of two interpretations of the relevant causal relationship. Either (1) pious things are loved by the gods because those things are pious, or (2) it is the gods’ love of those things that makes those things pious. Socrates argues by way of several examples that a thing can be in the state of being loved by the gods only through the gods’ act(s) of loving it, and Euthyphro agrees. Euthyphro also agrees with Socrates’ next claim: the gods love pious things because those things are pious, i.e., in response to their recognition that those things are pious.
But if a thing’s being pious were really identical with its being in the state of being loved by all the gods, as Euthyphro claimed at the outset, then we have a contradiction. For this claim commits Euthyphro to the view that the gods’ act(s) of loving a thing are what make that thing pious (Socrates calls this theophiles), but he has also assented to the claim that the gods’ recognition of a thing’s piousness is what makes them love it (Socrates calls thisosion). And these are clearly two very different claims. Socrates argues that the way out of this mess is to abandon Euthyphro’s initial identity claim. The most that such a claim could show is that pious things all share the particular feature of being loved by all the gods. But this is just to point out a mere attribute of pious things and not to tell us anything informative about the essence or nature of piety itself, i.e., about what makes a thing pious. If Socrates’ argument is correct, then our inquiry into the nature of piety (or, in more contemporary terms, into the nature of goodness or rightness) can, and indeed must, proceed independently of any claims about what the gods love (or, again in more contemporary terms, what God has ordained, commanded, etc.).