The problem in the Euthyphro is Euthyphro’s own beliefs

In the dialogue Euthyphro, Socrates forces Euthyphro’s beliefs to a series of paradoxes, and in each case it seems that the only problem is that Euthyphro believes the wrong side of the paradox.  

If divine beings have different beliefs about good and evil, then what the gods love is not holy (8e).

(corollary, if divine being can have different wills for any reason, then holiness would not be necessarily a good) 

If divine beings are not the first cause of goodness, then a consideration of the gods is completely unnecessary when considering holiness (11b).

In the first, it is more reasonable to deny the consequent. In the second, it is necessary to do so. Who can define holiness without speaking of God or the gods?

If piety is a kind of service, it cannot give the gods some benefit (13c) or have any product (14) or give the gods a benefit in any way (15).

In both of these, it is necessary to affirm the antecedent, for piety or holiness involves doing something.  

Either the gods lack something, or what the gods love is holy.

More reasonable to affirm the second part, for the very imposition of the word “holy” is to signify those things loved by gods, while the imposition of the word “god” or “gods” is to speak to beings lacking nothing.

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