The natural first question for a divine command theorist is whether God has the power to make horrible acts obligatory just by commanding that we perform them. So, some question such as this:
Can God make it the case that gratuitously torturing an infant is morally obligatory?
Following the work of Robert Adams, Edward Wierenga, and others, the standard response of divine command theorists has become something like this:
Since he is omnibenevolent, God would not command that we gratuitously torture infants.
Now it is important to note that this response only says that God would not issue such a command, it does not really answer the question. What we want to know is whether making gratuitous torture morally obligatory is something that God can do. Sure, God may be constrained by his love in such a way that some commands are beyond his capacity to issue (though how that squares with his omnipotence is an interesting question), but, regardless, he has the power to utter the words “Thou shalt torture an infant for no reason.” I know he has this power because humans have this power and God has the power to do anything that it is logically possible to do. So, we want to know, what would happen if God issued this command? Would gratuitous torture be obligatory?
Rather than pursue this tack, I want to suggest a slightly different direction to the inquiry. Let us now ask,
Is it logically possible to make an action morally obligatory just by commanding that it be performed?
The divine command theory says yes, there is one being for whom this is logically possible: God. God can (and has) made actions morally obligatory by commanding that we do them.
Is it logically possible to make treating one’s neighbor as one would like to be treated morally obligatory?
Again, the divine command theorist says yes, does he not? Some will even claim that God has done this.
Is it logically possible to make the gratuitous torture of an infant morally obligatory just by commanding that it be done?
How does the divine command theorist respond? This is a genuine question and I am curious to hear responses from those who espouse the theory. For now, however, I will continue the dialogue by making some educated guesses. The divine command theorist responds:
Such a thing is not logically possible. God would never give such a command.
Now the questions is:
Is it impossible to make the torture of infants morally obligatory because, since he is all-loving, God will not command that we torture infants, or is it impossible for to make infant torture morally obligatory because it is not logically possible for infant torture to be morally obligatory?
If the answer is (b) infant torture cannot be made obligatory because it is not logically possible for infant torture to be morally obligatory, then there is standard of wrongness that is independent of God and the divine command theory is false. (b) implies that, for some actions, it is just not logically possible that they are obligatory; no divine command is necessary.
If the answer is (a) infant torture cannot be made obligatory because God will not issue such a command, the next question is:
Suppose there exists a deity that has all the powers that God has but who is not constrained by omnibenevolence. If such a deity issues a command to gratuitously torture infants, would that make it obligatory to torture infants?
If the divine command theory is to escape the arbitrariness charge, the answer to this question had better be no. But the the question is why not?