Socrates: And what do you say of piety, Euthyphro? Is not piety, according to your definition, loved by all the gods?
Socrates: Because it is pious or holy, or for some other reason?
Euthyphro: No, that is the reason.
Socrates: It is loved because it is holy, not holy because it is loved?
This is called the "Euthyphro dilemma." Socrates seems to have to have trapped Euthyphro into choosing between two unattractive horns: is something good because the gods willed it, or did the gods will it because it is good? Are the gods higher than goodness, making goodness arbitrary and capricious? Or is goodness above the gods, making them submissive to it?
Bertrand Russell famously summarized the problem as applied to contemporary theists, in his "Why I Am Not a Christian":
If you are quite sure there is a difference between right and wrong, you are then in this situation: Is that difference due to God's fiat or is it not?
If it is due to God's fiat, then for God Himself there is no difference between right and wrong, and it is no longer a significant statement to say that God is good.
If you are going to say . . . that God is good, you must then say that right and wrong have some meaning which is independent of God's fiat, because God's fiats are good and not good independently of the mere fact that he made them.
If you are going to say that, you will then have to say that it is not only through God that right and wrong came into being, but that they are in their essence logically anterior to God.
The so-called dilemma has been answered numerous times.
For example, in his response, John Frame writes:
God's Word and God's goodness are equally ultimate aspects of his character. . . [C]ontrary to Euthyphro, neither Word nor goodness comes before the other; the two are correlative. There is nothing in God's nature which His Word does not express; and there is nothing in His Word which lacks truth. So: God's goodness determines God's revelation, and God's revelation determines His goodness.
Greg Koukl puts it like this:
The Christian rejects the first option, that morality is an arbitrary function of God's power.
And he rejects the second option, that God is responsible to a higher law. There is no Law over God.
The third option is that an objective standard exists (this avoids the first horn of the dilemma). However, the standard is not external to God, but internal (avoiding the second horn). Morality is grounded in the immutable character of God, who is perfectly good. His commands are not whims, but rooted in His holiness.
I agree with these responses. But the Christian apologist shouldn't stop there. He should also challenge the skeptic's own account of goodness. (I have a vague recollection of hearing an apologist make this point before, but have been unable to locate a source). For example, we could take Russell's wording and substitute ourselves in place of God:
If you are quite sure there is a difference between right and wrong, you are then in this situation: Is that difference due to your fiat or is it not?
If it is due to your fiat, then for you yourself there is no difference between right and wrong, and it is no longer a significant statement to say that you are good.
If you are going to say . . . that you are good, you must then say that right and wrong have some meaning which is independent of your fiat, because your fiats are good and not good independently of the mere fact that you made them.
If you are going to say that, you will then have to say that it is not only through you that right and wrong came into being, but that they are in their essence logically anterior to yourself.
Put simply, we can ask the skeptic who doubts the divine command understanding of ethics: is something good because you (or your community) willed it, or did you (or your community) will it because it is good? If the former, then goodness is arbitrary; if the latter, then goodness is objective, independent, external, and something to which we must submit.