the independence problem = if it is true that morally good acts are willed by God because they are morally good, this suggests that moral facts are independent of God's will
this is denied by DCT as it holds that all morality is dependent on God
the emptiness problem = if it is true that morally good acts are morally good because they are willed by God, there is no reason to care about God's moral goodness
the problem of abhorrent commands = if it is true that morally good acts are morally good because they are willed by God, there is no reason to worship him
the arbitrariness problem = rejects that morally good acts are good because they are willed by God, as God could command anything and it would be morally right e.g. genocide