The Main Argument of the Euthyphro

1. The gods love holy actions. But why do they love them? [10d]
2. The gods love holy actions because these actions are holy. (Why else?) [10d]
3. Now, according to Euthyphro, “holy” = “loved by the gods”. [10e-11a]
4. Therefore, the gods love holy actions because these actions are loved by the gods.
5. But in general, if x is V-ed by y (where V is a verb), then x is V-ed by y because y V-s x. [10b]
6. Hence, the holy actions are loved by the gods because the gods love them.
7. But we cannot have both A because of B and B because of A, so (4) and (6) are incompatible.